Point spread function optimization in SPECT

In this paper we propose a novel method for collimator design in single photon emission tomography (SPECT). The challenge here is to find a practical collimator design that allows good recovery and good sensitivity. Instead of working on the collimator\´s shape, the problem is addressed by optimizing the point spread function (PSF) with respect to the performance of the reconstruction algorithm in terms of resolution modelling. The optimization is based on an object-dependent cost function that takes into account bother recovery coefficient (RC) and sensitivity. Therefore, for each object considered a different "optimal" PSF is expected. Once a PSF is obtained, we assess its performances by plotting the coefficient of variation (COV) versus the recovery coefficient (RC) at each iteration of a maximum likelihood maximization expectation (MLEM) algorithm. We performed our experiments on two-dimensional (2-D) geometric phantoms, in order to investigate the relationship between the optimal PSF and the object geometrical properties, as well as on a 2-D brain activity phantom. We show that the optimized PSF\´s lead to resolution models that improve both image resolution and signal to noise ratio.